Tree visualization system and method based upon a compressed half-plane model of hyperbolic geometry

ABSTRACT

A node-link structure is displayed within a display area having a narrow rectangular shape with an edge along one side acting as a horizon of a hyperbolic space half-plane. Lower level node features that share a parent node feature have centers of area positioned on the display in order along a line parallel with the horizon, with sufficiently similar spacings along an axis perpendicular to the horizon from the region around a parent node feature, and with sufficiently similar spacings in a dimension parallel to the horizon from adjacent node features along the line, that the lower level node features sharing the parent node feature are perceptible as a group of related node features. The half-plane model with compression is used for layout of the node-link data, and the hyperbolic layout data is mapped to a Euclidean space for display.

RELATED APPLICATIONS

This application is a continuation of application Ser. No. 09/901,414filed 9 Jul. 2001.

LIMITED COPYRIGHT WAIVER

A portion of the disclosure of this patent document contains material towhich the claim of copyright protection is made. The copyright owner hasno objection to the facsimile reproduction by any person of the patentdocument or the patent disclosure, as it appears in the U.S. Patent andTrademark Office file or records, but reserves all other rightswhatsoever.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention provides a focus+context technique for visualizinglarge hierarchies; and more particularly provides for visualization of ahierarchy using a compressed half-plane model of hyperbolic geometry.

2. Description of Related Art

A focus+context technique for visualizing large hierarchies is describedin U.S. Pat. No. 5,590,250, entitled “Layout of Node-link Structures inSpace with Negative Curvature,” in U.S. Pat. No. 6,108,698, entitled“Node-Link Data Defining a Graph and a Tree Within the Graph,” and inU.S. Pat. No. 5,619,632, entitled “Displaying Node-link Structure withRegion of Greater Spacings and Peripheral Branches.” Related prior artpatent applications include:

-   Local Relative Layout of Node-Link Structures in Space with Negative    Curvature. John Lamping, Ramana Rao, Tichomir Tenev. EP Publication    No. 0977155, 2 Feb. 2000.-   Mapping a Node-Link Structure to a Rendering Space Beginning from    and Node.-   Ramana Rao, John Lamping, Tichomir Tenev. EP Publication No.    0977153, 2 Feb. 2000.-   Controlling Which Part of Data Defining a Node-Link Structure is in    Memory. Tichomir Tenev, John Lamping, Ramana Rao. EP Publication No.    0977131, 2 Feb. 2000.

The prior art patents listed above, and the references cited in suchpublications, provide substantial background information about the stateof the art, and reference is made to them for this purpose.

Prior art techniques described above can be understood by reference toFIG. 1. In the view of FIG. 1, a tree visualization consists of anode-link structure mapped into hyperbolic space and projected into aunit disc, resulting in a circular or elliptical view of the tree. Bymapping the tree into hyperbolic space with a closed horizon defined bythe unit disc, the entire tree is contained within an area that can bedisplayed all at once. The node-link structure in this example is anorganization chart, with nodes for individuals in the organization. Themapping tends to focus on nodes in the center of the display, with nodesdistant from the nodes in the center compressed into space approachingthe rim in a manner that preserves some context about the position ofthe nodes in the center, relative to the rest of the hierarchy.

The original circle view is a pure focus+context visualization, with afocus area in the center and a context area around the rim. The priorart technique results in a view best utilized when the circular view ofthe tree can be presented effectively within the form factor of thedisplay being used. However, when the display being used allows a narrowrectangle for display of the tree, the circular view of the unit discmust be distorted as shown in FIG. 1, to make best use of the space inthe display area. When the unit disc is distorted, more space isallocated arbitrarily to nodes along the long axis of the ellipse, andthe quality of the visualization suffers.

SUMMARY OF THE INVENTION

The present invention adapts the hyperbolic tree browser methods to thehalf-plane model of hyperbolic geometry, as described, for example, in“The Poincaré Half Plane, A Gateway to Modern Geometry”, by Saul Stahl,Jones and Bartlett publishers, 1993. By adapting the hyperbolic tree tothe half-plane model, a system is provided that makes efficient use ofnarrow display areas.

Just as in the prior art hyperbolic tree browser, the invention lays outa node-link structure in hyperbolic space, and then maps the hyperbolicspace into Euclidean space for display, and changes focus by changingthat mapping. However, various embodiments of the present inventiondiffer from the prior art for one or more reasons, including forexample:

The use of the half-plane model to represent locations in hyperbolicspace.

Basing layout on horocycles or lines, rather than circles or arcs.

Doing a different style of orientation preserving transformation.

The use of a compressed half-plane model to display the tree.

User interaction adjustments to tune the user interaction.

The present invention provides methods and systems for browsing anode-link structure which involves displaying representations of thenode-link structure within a display area, which are well suited toutilization of display areas with a narrow rectangular shape. Ananimated view of the node-link structure is accomplished, whichpreserves focus and context for the user, and allows scrolling amongrelated nodes. Thus, one embodiment of the invention is a method whichinvolves obtaining node-link data defining a node-link structure. Thenode-link structure includes nodes and links, where each link relates atleast two of the nodes. The node link data is used to present a sequenceof representations of the node-link structure on a display. The displayhas an edge along one side acting as a horizon corresponding for examplewith the horizon in the half-plane model of hyperbolic space. Thehorizon is preferrably the right side to preserve a left to rightorientation like that of a table, but may be for example the bottom sideto preserve a top to bottom orientation like that of a hierarchy ortree. The sequence begins with a first representation and ends with thelast representation. The last representation is perceptible as changedcontinuation of the first representation. Each representation in thesequence includes bounded node features representing nodes in thenode-link structure. A bounded node feature has a position in therepresentation on the display and a region of allocated display areaaround the position.

The bounded node features of each representation include a subset ofmore spaced node features. The nodes represented in at least one of thefirst and last representations form at least one peripheral branch inthe node-link structure. Each peripheral branch includes a top-level andat least one lower level. The top-level includes a top-level node andthe lower levels include lower level nodes that are not in therepresentation's subset of more spaced node features. Each node at thelower level has a parent node at a next higher level to which the nodeis related through one link. Lower level node features that share aparent node feature are arranged in a column, and have centers of areapositioned on the display in order approximately along a line generallyparallel with the horizon. The node features in the column havesufficiently similar spacings along an axis perpendicular to the horizonfrom the region around a parent node feature, and sufficiently similarspacings in a dimension generally parallel to the horizon from adjacentnode features along the line, that the lower level node features sharingthe parent node feature are perceptible as a group of related nodefeatures. Also, node features in a particular level of the hierarchy arearranged generally so that they appear to be in the same column as othernode features in the same level.

Animation of the representations can be understood by characterizing therepresentations according to “convex hulls” which are determined bygroups of nodes in the representation. The regions around the positionsof the bounded node features in each representation together determine afirst convex hull for the representation. The first convex hull enclosesa total area for the representation. The regions around the positions ofthe more spaced node features determine a second convex hull for therepresentation. The second convex hulls of the first and lastrepresentations enclose a sufficient portion of the available displayarea to act as a focus on the nodes within the second convex hull. Forexample, the “sufficient portion” is from about one-fourth to aboutthree-fourths of the available area, in a preferred embodiment. Thesecond convex hulls of the first and last representations includesubsets of bounded node features that represent different sets of nodes.The sequence of representations produces a perception that at least onebounded node feature has a nearest node spacing that increases from thefirst representation to the last representation (e.g. moves into thesecond convex hull) and that at least one other bounded node feature hasa nearest node representation that decreases from the firstrepresentation to the last representation (e.g. moves out of the secondconvex hull).

The set of nodes within a second convex hull can include any combinationof nodes in the node-link structure, including for example a node in onelevel of the tree and its children in next level of the tree, or a node,a subset of its children and a subset of its grandchildren, or multiplenodes in one level of the tree, with a subset of children of one or moreof the multiple nodes. In addition, more than one second convex hull maybe defined in a single first convex hull.

In one embodiment of the invention, the node-link data is used topresent one or more displayable representations, or alternatively togenerate display layout data for displayable representations, accordingto a method which includes storing hyperbolic layout data specifyingpositions of nodes in the node-link structure in hyperbolic space,accepting user input indicating a portion of said node-link structurefor display, using the half-plane model with compression to map thehyperbolic layout data for the portion of the node-link structure intodisplay layout data, and storing, transmitting or using said displaylayout data to display said representations.

Applying the half-plane model with compression includes mapping theselected portion of the hyperbolic layout data to a Euclidean spaceaccording to a half-plane model to produce Euclidean layout data. TheEuclidean layout data is then compressed as positions approach thedisplayable boundaries at the side of the display area opposite to thehorizon, to yield the display layout data. The compression preservesadditional context for upper level nodes in the node link structure,which may be lost outside the boundary of the display without thecompression.

The hyperbolic layout data in one embodiment comprises the datastructure associated with the nodes in the node-link structure whichincludes parameters specifying a position in the hyperbolic spacerelative to a parent node. In this manner, given a position on thedisplay which maps to a position in the hyperbolic space, the entiretree can be laid out.

In one embodiment, the data structure parameters are produced bydetermining, for each particular node, a distance along a first axisgenerally perpendicular to the horizon (referred to herein as “depth” inthe half-plane of hyperbolic space) between the parent node and theparticular node, and determining an offset along a second axis generallyparallel to the horizon (referred to herein as the “width” in thehalf-plane of hyperbolic space) from the parent node to the particularnode. The distance according to one aspect is determined by determininga number of child nodes including the particular node associated withthe parent, and determining a width along the second axis for each ofthe child nodes. The distance along the first axis is computed inresponse to the widths of the child nodes, so that groups of child nodeswhich require a greater width in the hyperbolic space are positioned agreater distance along the first axis (depth) away from their parents.

In an embodiment in which the data structure associated with the node inthe node-link structure includes parameters specifying a position inhyperbolic space relative to another node, the process of accepting userinput includes receiving an indication of the position in one of thehyperbolic space and the Euclidean space, finding a new position of afirst node in the node link structure close to indicated position, oralternatively receiving an indication at the position of the first nodein one of the hyperbolic space and the Euclidean space, and thencomputing the positions of other nodes in the node-link structurerelative to the first node. A changed representation is displayed basedupon the new position of the first node and the other nodes.

According to yet other embodiments, the displayed representation isdisplayed in a finite display area, and a process of accepting userinput includes excepting signals pointing to a location in the displayarea, and filtering user input in response to the location in thedisplay area to indicate a position hyperbolic space. In one embodiment,if the location is within a threshold distance in Euclidean space fromthe side of the display corresponding to the horizon, then a position issignaled at a location spaced away from the side corresponding to thehorizon. In another embodiment, if the location is within a regionadjacent the horizon, the position for the node is signaled at locationsufficiently spaced away from the side corresponding to the horizon ofthe display area to allow for display of a child of the node within thedisplay area. In another embodiment, if the location is within thecentral region of the display, then a position is signaled which resultsin display of a second representation of the node at location shiftedvertically within the display area from the first representation,preferrably in a manner that preserves the illusion of columns. Inanother embodiment, if the location is within a region along a sideopposite the horizon, then the position is signaled at location spacedaway from the side opposite the horizon by a predetermined distance.

The invention provides methods supporting a direct manipulation browserfor trees and tree-like graphs, particularly for narrow display areas.In the invention, there is a combination of focus+context and scrolling.Sibling nodes are in focus in the center, their descendants are incontext on the right (or toward the horizon), and their ancestors incontext on the left (or away from the horizon). The user can dragvertically (or parallel to the horizon) to scroll among siblings (SeeFIGS. 3 to 5 below), and they can drag horizontally to move betweenlevels of the hierarchy (See FIGS. 6 to 8 below). In addition todragging, a user can click on a node to bring it into focus. Clicking ona node in one embodiment causes the node to be centered vertically. Thusa scrolling effect can be achieved by clicking.

The vertical tree according to embodiments of the present invention,tries to maintain an illusion of columns, where not only the children ofone parent line up (along axis parallel to horizon), but grand-childrenand great-grand-children more-or-less line up in respective lines,creating an illusion of columns. User interactions tend to support thisillusion of columns as well, by ignoring small variations in horizontaldirection, giving a little resistance to horizontal motion. When a nodeis clicked, the node is generally centered vertically, unless the nodeis too near an edge

This visualization shares many of the advantages of the originalhyperbolic tree view. It does sacrifice having all the nodes of the treeconfined within a closed space (and visible if the lower level nodes donot compress against the edges too much), but it preserves displaying acontext of the nodes in focus, and having a smooth, intuitivemanipulation. It makes better use of screen real-estate, and is morecompatible with the left-to-right nature of textual labels.

In addition to being advantageous because of suitability for displayswith a rectangular aspect ratio (or other narrow shape), the interactionof scrolling/focusing by columns according to the present inventionmakes it very easy for people to reliably move up/down and across thenode-link structure in a very predictable and reliable way, supporting arectilinear pattern of the required clicking for moving around in thenode-link structure as it is presented in a sequence of displayedrepresentations.

While the invention works in any aspect ratio of window, its advantagesare especially important in a narrow form factor, where the originalhyperbolic tree is less useful. Since many applications only have roomfor a narrow form factor navigation display, this invention allows thehyperbolic tree visualization to be used in many more applications.

Other aspects and advantages of the present invention can be seen onreview of the figures, the detailed description and the claims whichfollow.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates prior art display of the hyperbolic tree mapped intothe unit disc, on a narrow form factor display area.

FIG. 2 illustrates display of the hyperbolic tree according to thehalf-plane model of the present invention.

FIG. 3 illustrates display of the hyperbolic tree according to thepresent invention using the half-plane model with compression, andtogether with FIGS. 4 and 5 shows scrolling of the tree.

FIG. 4 illustrates display of the tree of FIG. 3 scrolled vertically,changing the focus to the among siblings in the tree within the centralregion of the display.

FIG. 5 illustrates display of the tree of FIG. 3 scrolled vertically byan additional amount.

FIGS. 6-8 show display of the hyperbolic tree according to thehalf-plane model with compression with focus shifting horizontally froma first level of the tree to a lower level of the tree.

FIGS. 9 and 10 are schematic views showing how areas occupied by thenode features determine convex hulls.

FIG. 11 is a flow chart showing general acts in presenting a sequencerepresentations like the ones in FIGS. 3-5 and FIGS. 6-8.

FIG. 12 is a schematic diagram showing general components of a machinethat presents a sequence of representations like the ones in FIGS. 3-5and FIGS. 6-8.

FIG. 13 is a schematic block diagram showing components of a system thatcan present a sequence of representations of a node-link structureaccording to the present invention, and can produce layout data basedupon the half-plane model of the hyperbolic tree.

FIG. 14 is a flow chart showing acts in producing a displayablerepresentation of a node-link structure according to the presentinvention.

FIG. 15 is a schematic used for illustrating layout data according toone embodiment of the present invention.

FIG. 16 is a diagram illustrating regions of a display area used infiltering input signals from pointers accorded one aspect of the presentinvention.

FIG. 17 is a flow chart illustrating a process for filtering inputsignals from a pointer in one embodiment of the present invention.

FIG. 18 is a flow chart illustrating a process for filtering inputsignals from a pointer in one embodiment of the present invention.

DETAILED DESCRIPTION

The detailed description of embodiments of the present invention isprovided with reference to FIGS. 2-18.

The architecture of a preferred embodiment of the invention is like thatof the hyperbolic tree browser where the tree is mapped to a unit disc,rather than the half-plane of the present invention, and can beimplemented using technologies described in the patents referencedabove.

In a preferred embodiment, node positions in hyperbolic space arerepresented by a position in the half-plane model. The invention couldbe practiced with any representation of node positions in hyperbolicspace, but the use of the half-plane model makes many of thecalculations simpler. While the standard half-plane model uses the upperhalf-plane, it is more convenient in some embodiments use the lefthalf-plane, with the y axis as the horizon of the half-plane. This ismore conducive to a narrow form factor.

A. Conceptual Framework

The following conceptual framework is helpful in understanding the broadscope of the invention, and the terms defined below have the indicatedmeanings throughout this application, including the claims.

The term “data” refers herein to physical signals that indicate orinclude information. When an item of data can indicate one of a numberof possible alternatives, the item of data has one of a number of“values.” For example, a binary item of data, also referred to as a“bit,” has one of two values, interchangeably referred to as “1” and “0”or “ON” and “OFF” or “high” and “low.”

The term “data” includes data existing in any physical form, andincludes data that are transitory or are being stored or transmitted.For example, data could exist as electromagnetic or other transmittedsignals or as signals stored in electronic, magnetic, or other form.

“Circuitry” or a “circuit” is any physical arrangement of matter thatcan respond to a first signal at one location or time by providing asecond signal at another location or time. Circuitry “stores” a firstsignal when it receives the first signal at one time and, in response,provides substantially the same signal at another time. Circuitry“transfers” a first signal when it receives the first signal at a firstlocation and, in response, provides substantially the same signal at asecond location.

A “data storage medium” or “storage medium” is a physical medium thatcan store data. Examples of data storage media include magnetic mediasuch as diskettes, floppy discs, and tape; optical media such as laserdiscs and CD-ROMs; and semiconductor media such as semiconductor ROMsand RAMs. As used herein, “storage medium” covers one or more distinctunits of a medium that together store a body of data.

-   For example, a set of floppy discs storing a single body of data    would together be a storage medium.

A “storage medium access device” is a device that includes circuitrythat can access data on a data storage medium. Examples include drivesfor reading magnetic and optical data storage media.

“Memory circuitry” or “memory” is any circuitry that can store data, andmay include local and remote memory and input/output devices. Examplesinclude semiconductor ROMs, RAMs, and storage medium access devices withdata storage media that they can access.

A processor performs an operation or a function “automatically” when itperforms the operation or function independent of concurrent humancontrol.

Any two components are “connected” when there is a combination ofcircuitry that can transfer signals from one of the components to theother. For example, two components are “connected” by any combination ofconnections between them that permits transfer of signals from one ofthe components to the other.

A processor “accesses” an item of data in memory by any operation thatretrieves or modifies the item, such as by reading or writing a locationin memory that includes the item. A processor can be “connected foraccessing” an item of data by any combination of connections with localor remote memory of input/output devices that permits the processor toaccess the item.

A processor or other component of circuitry “operates on” an item ofdata by performing an operation that includes obtaining a resulting itemof data that depends on the item of data operated on. For example, theresulting item of data could result from an operation that accesses theitem of data operated on or from a logic or arithmetic operation on theitem of data operated on.

An operation, such as an operation of a processor or other circuitry,“uses” an item of data when the manner in which the operation isperformed depends on the value of the item.

An “instruction” is an item of data that a processor can use todetermine its own operation. A processor “executes” a set ofinstructions when it uses the instructions to determine its operations.

A “program” is an item of data that indicates a sequence of instructionsthat a processor can execute.

To “obtain” or “produce” an item of data is to perform any combinationof operations that begins without the item of data and that results inthe item of data. An item of data can be “obtained” or “produced” by anyoperations that result in the item of data. An item of data can be“obtained from” or “produced from” other items of data by operationsthat obtain or produce the item of data using the other items of data.

A first item of data “indicates” a second item of data when the seconditem of data can be obtained from the first item of data. The seconditem of data can be accessible using the first item of data. Or thesecond item of data can be obtained by decoding the first item of data.Or the first item of data can be an identifier of the second item ofdata. For example, an item of data may indicate a set of instructions aprocessor can execute or it may indicate an address.

An item of data “indicates” a thing, an event, or a characteristic whenthe item has a value that depends on the existence or occurrence of thething, event, or characteristic or on a measure of the thing, event, orcharacteristic.

An item of data “includes” information indicating a thing, an event, ora characteristic if data indicating the thing, event, or characteristiccan be obtained by operating on the item of data. Conversely, an item ofinformation that indicates a thing, an event, or a characteristic can besaid to “include” an item of data if data indicating the thing, event,or characteristic can be obtained by operating on the item of data.

An operation or event “transfers” an item of data from a first componentto a second if the result of the operation or event is that an item ofdata in the second component is the same as an item of data that was inthe first component prior to the operation or event. The first component“provides” the data, and the second component “receives” or “obtains”the data.

“User input circuitry” is circuitry for providing signals based onactions of a user. User input circuitry can receive signals from one ormore “user input devices” that provide signals based on actions of auser, such as a keyboard or a mouse. The set of signals provided by userinput circuitry can therefore include data indicating mouse operationand data indicating keyboard operation. Signals from user inputcircuitry may include a “request” for an operation, in which case asystem may perform the requested operation in response.

An “image” is a pattern of physical light. An “image output device” is adevice that can provide output defining an image. A “display” is animage output device that provides information in a visible form. Adisplay may, for example, include a cathode ray tube; an array of lightemitting, reflecting, or absorbing elements; a structure that presentsmarks on paper or another medium; or any other structure capable ofdefining an image in a visible form.

To “present an image” on a display is to operate the display so that aviewer can perceive the image.

When an image is a pattern of physical light in the visible portion ofthe electromagnetic spectrum, the image can produce human perceptions.The term “graphical feature”, or “feature”, refers to any humanperception produced by, or that could be produced by, an image.

A “pointer” is a graphical feature that indicates a position within animage. A pointer is “at a position” when the pointer is indicating theposition.

A “pointer control device” is a user input device that can be used tocontrol position of a pointer within an image presented on a display.Examples of pointer control devices include a mouse, a joystick, a trackball, a portion of a keyboard with directional keys, and so forth. Anaction of a user “moves a pointer” if the action causes a pointercontrol device to provide signals causing a change in position of thepointer.

In general, an action by a user “indicates” a thing, an event, or acharacteristic when the action demonstrates or points out the thing,event or characteristic in a manner that is distinguishable from actionsthat do not indicate the thing, event, or characteristic. The user can,for example, use a pointer control device such as a mouse to indicate aposition by positioning a pointer at the position and clicking a buttonon the pointer control device while the pointer is at the position.

An image “shows” or “includes” a feature when the image produces, orcould produce, a perception of the feature.

An item of data “defines” an image when the item of data includessufficient information to produce the image, such as by presenting it ona display. An item of data “defines” a feature when the item defines oneor more images that show or include the feature.

A “structure” is a group of items, all of which are related to form aunity. A “node-link structure” is a structure that includes items callednodes and links. Each link relates two or more of the nodes. Two nodesare “related through one link” or “related through a link” if thenode-link structure includes a link that relates the two nodes. A link“relates a pair” of nodes if the link relates only two nodes.

A “graph” is a node-link structure in which each link relates two nodes.An “acyclic graph” is a graph in which there are no loops of edges. A“directed graph” is a graph in which each link indicates directionbetween the nodes it relates, with one node being a source of the linkand the other being a destination. A “tree” is an acyclic directed graphwith exactly one root node such that every other node in the tree can bereached by only one path that begins at the root node and follows eachlink in the path in its indicated direction.

A “branch” of a node-link structure is a set of nodes that forms a treewithin the node-link structure if the links are treated as relatingpairs of nodes and as indicating direction. A branch therefore includestwo or more levels, with the “top level node” being the node that is theroot node of the tree formed by the branch, and “lower level nodes”being nodes at one or more levels of the tree below the top level node.Each lower level node has a “parent node” at the next higher level towhich the lower level node is related through one link. A parent nodehas a set of “child nodes” at the next lower level to each of which theparent node is related through one link. The child nodes of a parent“share” the parent node.

An item of data “defines” a node-link structure if the item of dataincludes information indicating how the links relate the nodes. Forexample, the item of data could include, for each link, an identifier ofeach of the nodes that it relates.

An item of data defining a node-link structure includes “content” if theitem of data includes information about nodes or links other thaninformation indicating how the links relate the nodes. For example, theitem of data could include a name or other descriptive information for anode or for a link.

A graphical feature “represents” a node-link structure when thegraphical feature itself includes features that map one-to-one with aset of nodes and links in the node-link structure.

A feature that maps to a node “represents” the node and a feature thatmaps to a link “represents” the link. A “node feature” is a feature thatrepresents only one node, and a “link feature” is a feature thatrepresents only one link.

A “graphical representation” or “representation” is a graphical featurethat includes elements that are spatially related in a configurationthat represents information.

A “sequence of representations” is a sequence that includes at least tworepresentations. A sequence of representations begins with a “firstrepresentation” and the first representation is followed by a “sequenceof at least one following representation” that ends with a “lastrepresentation.” Each following representation follows a “precedingrepresentation.” A sequence of representations may also include one ormore “intermediate representations” between the first and lastrepresentations. A sequence of representations may include a“subsequence of representations” that is also a sequence ofrepresentations as defined above.

A second display feature is perceptible as a “continuation” of a firstdisplay feature when presentation of the second display feature followspresentation of the first display feature in such a way that the userperceives the first display feature as being continued when the seconddisplay feature is presented. This can occur when the successive displayof two display features is so close in time and space that they appearto be the same display feature. An example of this is the phenomenoncalled “object constancy.”

The last representation of a sequence of representations is perceptibleas a “changed continuation” of the first representation when the lastrepresentation is perceptible as a continuation of the firstrepresentation but with at least one change. An intermediaterepresentation is similarly perceptible as an “intermediate changedcontinuation” of the first representation when the intermediaterepresentation is perceptible as a continuation of the firstrepresentation but with at least one change.

An “animation loop” is a repeated operation in which each repetitionpresents an image and in which features in each image appear to becontinuations of features in the next preceding image. If a user isproviding signals through user input circuitry, the signals can bequeued as events and each loop can handle some events from the queue. An“animation cycle” is a single iteration of an animation loop.

The “detail” with which an image is presented is the quantity ofinformation in the presented image. Information in an image can beincreased by providing additional lines or objects, by providing arcsrather than straight lines, and so forth. A “level of detail” is a valueindicating one of a set of quantities of information in an image.

Speed of presentation of images is “maintained” when a sequence ofimages is presented without a reduction in speed of presentation.

A sequence of images is presented at a sufficient speed that features inthe images are perceptible as a “continuously moving feature” if theimages can provide the perception of a single feature that moves, andmay also evolve, rather than the perception of a sequence of distinctfeatures presented in succession. Such a speed is sometimes referred toas an “animation speed.”

An operation includes a “sequence of iterations” when the operationincludes a sequence of substantially similar suboperations, eachreferred to as an “iteration,” where each iteration after the first usesstarting data produced by the preceding iteration to obtain ending data.Each iteration's ending data can in turn be used by the followingiteration.

An item of data “defines” a representation when the item defines animage that includes the representation. A representation “is presented”when an image that includes the representation is presented. Providingdata to a display “causes” presentation of a representation or sequenceof representations when the display responds to the data by presentingthe representation or sequence of representations.

A “region” of a representation is a bounded area of the representation;for example, a single point is the smallest possible region of anyrepresentation. A representation “includes” a feature or a region ifpresentation of the representation can produce perception of the featureor region.

A “representation of a node-link structure” is a graphicalrepresentation that represents the node-link structure. In arepresentation of a node-link structure, for example, link features canbe lines, such as arcs or straight lines, that extend between nodefeatures. A representation of a node-link structure may also includegraphical features that “indicate” content, such as words or otherstrings of characters from which a viewer can obtain information about arepresented part of the structure.

A representation of a node-link structure is “perceptible as a figure ona background” if the representation includes a feature, referred to asthe “figure,” and the feature appears to be on or above a region that isnot part of the figure, referred to as the “background.”

A “half-plane” is defined by a line in two-dimensional plane thatseparates the plane in two pieces; each one of this pieces is termed ahalf-plane. The line separating the two “half-planes” is termed the“horizon” in the half-plane model of hyperbolic space.

A coordinate system can be applied to a half-plane with two mutuallyorthogonal coordinate axis defined as “width axis” and the “depth axis”.The width axis is the axis running parallel to the horizon, and the“depth axis” is the axis running orthogonal to the horizon.

A point in a half-plane is said to be “deeper” than a second point if itis closer to the “horizon” than the first. Similarly, a point in ahalf-plane is said to be “shallower” than a second point if it isfarther away from the “horizon” than the first point.

A “bounded node feature” is a node feature that has a perceptibleboundary. The “center of area” of a bounded node feature is the centerof area of the region within the node feature's boundary. The positionof a bounded node feature's center of area can therefore be computedfrom the node feature's boundary or estimated by viewing therepresentation.

The “nearest other node feature” of a first bounded node feature in arepresentation is a second bounded node feature whose center of area isspaced along the depth axis of the half-plane, from the first nodefeature's center of area by a distance no greater than the spacing alongthe depth axis from the first node feature's center of area to any otherbounded node feature's center of area. The distance along the depth axisis referred to herein as the node feature's “nearest node spacing.”bounded node feature may have more than one nearest other node feature,all with centers of area at the nearest node spacing. A bounded nodefeature has a position and a node region around the position centered atthe node feature's center of area. The node region around the positionhas an area assigned for display of a representation of the node on thedisplay.

The “convex hull” determined by the positions and node regions aroundthe positions of two or more bounded node features in a representationis the smallest region that includes the node regions around thepositions and also includes every point on any straight line between twopoints in the region.

The “area of,” or the “area enclosed by,” a part of the representationis a measure of the part's two-dimensional extent.

A convex hull determined by positions and node regions around thepositions of bounded node features in a representation encloses “a totalarea for the representation” if along the depth axis of all bounded nodefeatures in the representation are included in the convex hull; such aconvex hull may be referred to as an “outer convex hull.” An “innerconvex hull” is a convex hull determined by positions and node regionsaround the positions of a subset of the bounded node features in arepresentation that encloses less than the total area for therepresentation. An inner convex hull encloses “approximately half therepresentation's total area” if the area enclosed by the inner convexhull is between approximately one-fourth and approximately three-fourthsof the total area for the representation. A representation may includemore than one subset of bounded node features with positions and noderegions around the positions that determine an inner convex hull thatencloses approximately half the representation's total area.

Bounded node features in a first region have nearest node spacings thatare “in general perceptibly greater” than in a second region if a viewercan see that the nearest node spacings are generally greater in thefirst region than in the second. A region in which bounded node featureshave nearest node spacings that are in general perceptibly greater thanin other regions of a representation may be referred to as a “region ofgreater spacings.”

A set of “more spaced node features” in a representation of a node-linkstructure is a set of bounded node features that determines an innerconvex hull that encloses approximately half the representation's totalarea and that also encloses a region in which bounded node features havenearest node spacings that are in general perceptibly greater than in aregion outside the inner convex hull.

A “peripheral branch” in a node-link structure that is represented by arepresentation that includes a set of more spaced node features is abranch that includes lower level nodes that are not represented by nodefeatures in the set of more spaced node features.

Centers of area of node features in a representation are “positionedapproximately along a line” if a line can be drawn within therepresentation such that each node feature's center of area is closer tothe line than to an adjacent node feature's center of area.

Lower level node features that share a parent node feature and whosecenters of area are positioned approximately along a line are positionedwith “sufficiently similar spacings from the center of area of theparent node feature and with sufficiently similar spacings from adjacentnode features along the line that the lower level node features sharingthe parent node feature are perceptible as a group of related nodefeatures,” if the lower level node features together appear to a viewerto be a group.

Inner convex hulls in the first and last representations of a sequenceinclude subsets of bounded node features that “represent different setsof node” if the set of bounded node features in the inner convex hull ofthe first representation and the set of bounded node features in theinner convex hull of the second representation are not identical.

A sequence of representations produces a perception that a node feature“has a nearest node spacing that increases from the first representationto the last representation” if a viewer can see that the node feature'snearest node spacing is larger in the last representation than in thefirst representation. Similarly, a sequence of representations producesa perception that a node feature “occupies a decreasing area from thefirst representation to the last representation” if a viewer can seethat the node feature's nearest node spacing is smaller in the lastrepresentation than in the first representation.

B. General Features

FIGS. 2-12 show general features of the invention. In FIG. 2, ahyperbolic tree is mapped onto a half-plane, so that the parent node 100has his children nodes 101-105 arranged generally along a vertical line.The children of the nodes 101-105 are compressed toward the horizon onthe right side of the display area 110, according to the hyperbolicgeometry. The displayed representation in FIG. 2 results from mappingthe layout from hyperbolic space according to half-plane model intoEuclidean space. As can be seen, the parent node 100 consumes arelatively large amount of the display area, and much context concerningother nodes related to the parent node 100 is lost.

FIG. 3 shows layout of the node link structure of FIG. 2, with theaddition of compression in the Euclidean space of features as theyapproach the edge (left side) of the display area 110 opposite thehorizon in the hyperbolic space. Thus, the parent node 100 appearscompressed, providing greater context than is available withoutcompression, where it may have been positioned outside the display area.Nodes 102 and 103, as well as the column defined by nodes 101-104, nearthe center of the display area, serve as the focus.

FIG. 3 along with FIGS. 4 and 5 illustrate scrolling among the siblings101-105 vertically in the display area, or along a line which isgenerally parallel to the horizon. Thus, the user may change the focusof the display from the node 102 of FIG. 3 to the node 103 a shown inFIG. 4 by scrolling vertically, while maintaining the position of thesiblings 101-105 along the axis perpendicular to the horizon. FIG. 5shows further scrolling, in which the node 105 moves into the region offocus, by vertical movement in the tree.

FIGS. 6-8 illustrate changing focus in the display as nodes are movedaway from the horizon. Thus, the parent node 100 and the children nodes101-105 are illustrated, where the children nodes lie essentially in thecentral region of the display. As the next level of children is movedinto focus as shown in FIG. 7, the nodes 101-105 are shifted toward theside of the display area 110 which is opposite the horizon, and detailsof the nodes near the horizon emerge. Also shown in FIG. 7, the siblingnode 106 emerges from outside the bottom side of the display area. Ascan be seen in FIG. 8, the parent node 100, and the sibling nodes101-106 are further compressed as they are shifted toward the left sideof the display area 110, and greater detail emerges from the sidecorresponding to the horizon.

With reference for example to FIGS. 6-8, an image generally 111 in FIG.6 shows a representation of a node-link structure, an image generally112 in FIG. 7 shows a representation of the same node-link structure,and an image generally 113 shows a representation of the same node-linkstructure. The representations provided by the images 111, 112 and 113each include node features that represent nodes in the node-linkstructure. Each node feature is a bounded node feature with a center ofarea and the nearest node spacing along the depth axis, that is the axisperpendicular to the horizon. The center of area, an allocated width ofthe feature along an axis parallel to the horizon, and the nearest nodespacing define a region allocated within the display area correspondingto the node.

The node features in the image 111 include node feature 103, with anearest node spacing larger than the nearest node spacing of its parentor of its children. Likewise the node features in the image 112 includenode feature 103, with a larger nearest node spacing toward itschildren, and having a content “Rachel” within the allocated region onthe display. The node 100 is a parent node related by one link to node103. The node 115 is a child node among a set of sibling nodes at thenearest node spacing for node 103, and related by one link to node 103.The nearest node spacing for node 103 toward its children nodes islarger than the nearest node spacing for node 115 for its childrennodes, and larger than the nearest node spacing for node 100 for itschildren nodes.

Although the representations provided by the images 111, 112 and 113 aredifferent, the representation in image 112 can be perceived as a changedcontinuation of the representation in image 111, and the representationin image 113 can be perceived as a changed continuation of therepresentation in image 112. FIGS. 6-8 illustrate that if therepresentation of image 113 is perceived as a changed continuation ofthe representation of image 112, which is in turn perceived as a changedcontinuation of the representation of image 111, the representationswill also produce the perception that the nearest node spacing of thenode feature 103 decreases, and the nearest node spacing of the nodefeature 115 increases as the sequence of representations in FIGS. 6-8 ispresented.

In addition, the representations of images 111-113 are presented with aregion of greater spacings generally in the central part of the displayarea, and with at least one peripheral branch associated with nodes inthe tree. The region of greater spacings in the representation of image111 can be seen as including node features 101-105 and 115. The regionof greater spacings in the representation of image 113 can be seen asincluding node features for 101-106 and node 115. Thus sets of nodeswithin the regions of greater spacings in the representations in images111-113 are not identical.

FIGS. 9 and 10 illustrate how a part of the representation that includesa region of greater spacings in accordance with the invention can bedistinguished from other parts of representation based upon the conceptof a convex hull. FIGS. 9 and 10 show a display area 130 which includesan edge corresponding to the vertical axis 131 corresponding to thehorizon of the hyperbolic half-plane. Axis 132 corresponds to the depthaxis, perpendicular to the horizon of the hyperbolic half-plane. Therepresentation within the display area 130 has node features, includinga root R, a second level of nodes A and B, and a third level of nodes,including nodes W-Z and to S-V. The regions on the display allocated forall the nodes define a first convex hull indicated by the dashed line134. The convex hull 134 encloses a total area for the representation inthe display area 130. The nodes R, A and B determine a second convexhull in FIG. 9 represented by the dashed line 135. The nearest nodespacing along the axis 132 between the root R and the children nodes Aand B is larger than the nearest node spacing between the children nodesA and B, and their children nodes in the next lower level of the tree.

In FIG. 10, the second convex hull is defined by the nodes having thelargest nearest node spacing, which includes the nodes A and B, andtheir children nodes W-Z and S-V. Thus, the second convex hull in FIG.10 is defined by the dashed line 136, and includes a different set ofnodes than are enclosed by the second convex hull in FIG. 9.

In FIG. 11, the act in box 120 begins by obtaining node-link datadefining a node-link structure. The node-link structure includes nodesand links, with each link relating at least two nodes.

The act in box 122 uses the node-link data obtained in box 120 topresent a first representation of the node-link structure. The firstrepresentation includes a region of greater spacings in which nearestnode spacings are in general perceptibly greater than in another region,as described above. The first representation also includes peripheralbranches in which node features that share a parent node feature areperceptible as a group of related node features, also as describedabove.

The act in box 124 then presents a next representation of the node-linkstructure. The next representation is perceptible as a changedcontinuation of the first representation. Like the first representation,the next representation includes a region of greater spacings in whichnearest node spacings are in general perceptibly greater than in anotherregion, as described above, but the regions of greater spacings of therepresentations include different subsets of node features. The nextrepresentation also includes peripheral branches in which node featuresthat share a parent node feature are perceptible as a group of relatednode features.

Presentation of representations as in FIG. 11 produces a perception thatthe nearest node spacings of some node features increase and the nearestnode spacings of others decrease.

As indicated by the dashed line in FIG. 11, the act in box 124 isincluded in one iteration, and additional iterations can be performed topresent different representations of the node-link structure ending witha last representation. In each iteration, the spacings change, resultingin a series of representations, each perceptible as a changedcontinuation of the first representation.

Machine 150 in FIG. 12 includes processor 152 connected for receivingdata indicating user signals from user input circuitry 154 and forproviding data defining images to display 156. Processor 152 is alsoconnected for accessing node-link data 158, which define a node-linkstructure. Processor 152 is also connected for receiving instructiondata 160 indicating instructions through instruction input circuitry162, which can illustratively provide instructions received fromconnections to memory 164, storage medium access device 166, or network168.

In executing the instructions indicated by instruction data 160,processor 152 uses node-link data 158 to provide first representationdata to display 156 to cause it to present a first representation of thenode-link structure.

The first representation includes a region with more spaced nodefeatures and peripheral branches in which children are perceptible as agroup of related node features, as discussed above in relation to FIGS.6-8.

In executing the instructions indicated by instruction data 160,processor 152 also receives user signal data from user input device 154indicating a change in the first representation.

In response, processor 152 automatically provides second representationdata to display 156 to cause it to present a sequence of at least onefollowing representation, ending with a last representation that isperceptible as a changed continuation of the first representation. Likethe first representation, the last representation includes a region withmore spaced node features and peripheral branches in which children areperceptible as a group of related node features, as discussed above inrelation to FIGS. 6-8. But the region of greater spacings in the lastrepresentation includes a different subset of node features than in thefirst representation, and presentation of the last representationproduces a perception that some nearest node spacings increase andothers decrease.

As noted above, FIG. 12 illustrates three possible sources from whichinstruction input circuitry 162 could receive data indicatinginstructions-memory 164, storage medium access device 166, and network168.

Memory 164 could be any conventional memory within machine 150,including random access memory (RAM) or read-only memory (ROM), or couldbe a peripheral or remote memory device of any kind.

Storage medium access device 166 could be a drive or other appropriatedevice or circuitry for accessing storage medium 170, which could, forexample, be a magnetic medium such as a set of one or more tapes,diskettes, or floppy discs; an optical medium such as a set of one ormore CD-ROMs; or any other appropriate medium for storing data. Storagemedium 170 could be a part of machine 150, a part of a server or otherperipheral or remote memory device, or a software product. In each ofthese cases, storage medium 170 is an article of manufacture that can beused in machine 150. Data units can be positioned on storage medium 170so that storage medium access device 166 can access the data units andprovide them in a sequence to processor 152 through instruction inputcircuitry 162. When provided in the sequence, the data units forminstruction data 160, indicating instructions as illustrated.

Network 168 can provide instruction data 160 received from machine 180.Processor 182 in machine 180 can establish a connection with processor152 over network 168 through network connection circuitry 184 andinstruction input circuitry 162. Either processor could initiate theconnection, and the connection could be established by any appropriateprotocol. Then processor 182 can access instruction data stored inmemory 186 and transfer the instruction data over network 168 toprocessor 152 so that processor 152 can receive instruction data 160from network 168. Instruction data 160 can then be stored in memory 164or elsewhere by processor 152, and can be executed.

C. Implementation

The general features described above could be implemented in numerousways on various machines to present representations of node-linkstructures. An implementation described below has been implemented on acomputer based on a Pentium class processor running the WindowsNToperating system, executing a C++/ActiveX or a JAVA program.Implementations on a Sun SPARCStation running a Unix/X operating system,or an Apple Macintosh personal computer could also be provided. The Uniximplementation executes instructions written in a JAVA programminglanguage, commercial versions of which are available from SunMicrosystems, Inc., Palo Alto, Calif.

FIG. 13 illustrates components of systems in which the invention maybeen implemented.

Machine 200 in FIG. 13 includes central processing unit (CPU) 202, amicroprocessor or other appropriate processor. CPU 202 is connected toreceive data indicating user signals from user input devices thatillustratively include keyboard 204 and mouse 206. CPU 202 is alsoconnected to provide data to cause presentation of images on display208.

Images presented on display 208 can include pointer 210 controlled bymouse 206 or another pointer control device.

CPU 202 is connected to one or more memory components that togetherprovide memory environment 220. The memory components conventionallyinclude resident RAM connected directly to CPU 202, one or more internaldisk drives or other storage medium access devices connected to CPU 202through an internal bus, and one or more external memory components suchas peripheral devices or remote servers that include storage mediumaccess devices and that are connected to CPU 202 through externalconnections of machine 200. CPU 202 conventionally accesses data storedin any memory component in environment 220 by providing addresses.

FIG. 13 illustratively shows program components and data componentsstored in memory environment 220; program and data components areillustratively shown separately, but need not be stored separatelywithin a given memory component. Program components include data thatindicate instructions CPU 202 can execute, and can be stored in objectcode form or source code form; if appropriate, the program componentscan also include any compilers and interpreters needed to obtaininstructions from program components stored in source code form. Inexecuting instructions indicated by program components, CPU 202 accessesand uses data components.

In executing instructions indicated by operating system program 230, CPU202 performs operations that transfer data between CPU 202 and othercomponents of machine 200. Such operations can include, for example,mapping logical addresses in the memory space of CPU 202 to physicaladdresses for accessing a memory component in environment 220.

In executing instructions indicated by JAVA environment program 232,which includes a JAVA virtual machine and other resources, CPU 202provides the standard JAVA interface. As a result, CPU 202 can executeJAVA programs, so that the tree browser interface program 234 andhyperbolic geometry program 236 can be implemented in JAVA.

In executing instructions indicated by browser interface program 234,CPU 202 first initializes machine 200. Then CPU 202 uses node-link data240 defining a node-link structure to obtain hyperbolic layout data 242,indicating positions for parts of the node-link structure in a layoutspace; in the current implementation, the layout space is a hyperbolichalf-plane. Then CPU 202 uses layout data 242 to obtain mapped data 244with compression in a Euclidean space for an initial representation ofthe node-link structure. CPU 202 provides data to display 208 to causepresentation of the initial representation.

In executing instructions indicated by browser interface program 234,CPU 202 also receives data indicating user signal events from keyboard204 and mouse 206. CPU 202 sets up, maintains, and handles a queue ofsteps for responding to an event by accessing event queue data 246. Whenthe steps responding to a user signal event are completed, CPU 202 canset up steps for responding to the next event.

In executing instructions indicated by browser interface program 234,CPU 202 can also modify animation parameters by accessing animationparameter data 248. Or CPU 202 can use layout data 242 to obtain mappeddata 244 for a changed representation of the node-link structure, thenprovide data to display 208 to cause its presentation.

CPU 202 can execute instructions indicated by hyperbolic geometryprogram 236 for various purposes, such as to obtain layout data 242, toobtain mapping data 244, and to map from a position of pointer 210 to apart of the node-link structure. As shown in FIG. 13, a representationcan include a background 250 on which an image 252 is shown, and aposition of pointer 210 within image 252 can be mapped to the nearestnode, for example.

In the prior hyperbolic tree, the layout algorithm is based on a nodehaving a wedge, centered at itself assigned to it to lay out itsdescendants. It then lays out its children in an arc centered on itselfand spanning that wedge, giving a subpiece of the wedge to each child.The subpieces and radius of the arc are chosen such that each childwould be sufficiently separated from other children and would get awedge inside the subpiece subsuming as large an angle is at wanted forits own children.

In this invention, it is preferable for children of a node to appear ina straight line, consistent with the more orthogonal feel of theinvention. In the figures, for example, the children of a node aredisplayed vertically aligned. This is achieved by laying out children ofnode on a horocycle, specifically, a horocycle represented by a lineparallel to the horizon. The transformations of the hyperbolic planeused by the invention will always map such horocycles to other suchhorocycles, thus preserving a vertical alignment of all children of anode.

The layout algorithm in one example, is based on a node having a sectionof horocircle, with the node at the midpoint, and with all area to theright of the horocircle in the half-plane assigned to lay out thedescendants of the node. In terms of the half-plane model with thehorizon on the right side of the display, the node is assigned avertical line segment. The node will lay out its children on a horocycleof the same family in the area assigned to it. In terms of thehalf-plane model, it will choose a vertical line segment to the right ofits line segment, and with the same height in the half-plane model. Thiswill make it have a longer length in the hyperbolic geometry. It willthen assign each child a subsegment of that horocycle, and place thechild at the center of its subsegment. The assignments are made so thateach child gets a minimum spacing from siblings, and gets the length ofhorocycle it wants to layout its own children.

Layout of the tree proceeds in the following manner in one preferredembodiment. (All distances are in hyperbolic distance units).

1. The root node is given an initial distance, which is usually 1.5, butcan be controlled from about 0.15 to 15, depending on “stretch factor”(this is a number between 0.1 and 10 that can be controlled by the userto their liking). Smaller number means that the rest of the tree will belaid out in a smaller space, leading to a more crowded tree.

2. Once a parent node is laid out, all its children can be then laidout. The parent node has already been assigned a width it can use foritself and its descendants.

-   -   a. Each child wants a certain space for itself (and its        descendants). This width on the width axis parallel to the        horizon (in hyperbolic distance) is given by:        width=Maximum(min_width,0.5*a sin h(n*0.2)))    -   where n is the number of children this child has.

The number min_width is the minimum allowable width, usually 0.2, butcan vary from 0.02 to 2.0, for example, depending on a “stretch factor”.A smaller number means more crowded tree.

Here, the function a sin h (inverse hyperbolic sine) is somewhatarbitrary, any similarly behaving function (such as log) can be used. Itneeds to grow as the number of children grows, but not proportionately,since we can be more width by placing the children farther on the depthaxis from the parent. Thus if a child has many children, the space isaccommodated partially by allocating more width, and partially byplacing the children farther on the depth axis from the parent.

-   -   b. Once the requested space for each child is computed, we know        the total width required. This is usually larger than the width        that the parent has. This is where the property of the        hyperbolic space becomes useful: by placing the children farther        away from the parent (toward the horizon), more hyperbolic space        can be obtained.

The amount of parent-child distance (the distance on the depth axis fromthe parent to the horocycle) to use is computed by the formula:dist=Maximum(min_dist, log((totalWidth+spacing)/parentWidth ))

The number min_dist is the minimum allowable distance, normally set to1.0, but can range from 0.1 to 10, for example. The number “spacing” isthe amount of “padding” to give between siblings of the parent. Usuallythis is set to 0.15, but this can also be adjusted (0.015-1.5).

-   -   c. Once the distance and total width are calculated, each child        is given a coordinate relative to the parent, so once the parent        is mapped to a point on a screen, the location of the child can        be easily computed.

3. Step 2 is repeated until all necessary nodes are laid out.

The constants mentioned in the procedure above are given default values,which after experimentation seems to offer good node density on thescreen. However, these can be adjusted to give better results forspecific trees.

Once these parameters have been calculated and stored in data structuresassociated with the nodes, the first child is placed on the child'shorocycle to give it its required width and radius from the edge of thechildren's horocycle. Then the position of each successive child on thehorocycle is calculated by adding the previously calculated inter-childdistances to the position of the previous child.

The positions can be recorded either as an absolute position or as arelative position, as described in the above-cited patents.

In the original hyperbolic tree, a click on a position indicates thatposition should be mapped to the center of the display. In the presentinvention it indicates that position should be mapped to the verticalcenter of the display, while maintaining the approximate horizontalposition. As with the original hyperbolic tree, the mapping chooses notonly a position to be at the center, but also an orientation. In thepresent invention, the orientation is chosen so that the points on theoriginal y-axis stay on the y-axis. This also causes the children of allnodes to be laid out toward the right.

Thus, after the layout procedure, the mapping is performed. In thepreferred embodiment, a mapping starts with some node N at the specifiedposition P, which is known before the mapping (for example, the userwants to center the node N). Each node is mapped to a point in an upperhalf-plane which represents a map of hyperbolic space. This point islater converted to actual screen coordinates after compression androtation by 90 degrees (so the x- and y-axes actually switch).

1. Move the node N to position P(x,y).

2. Map out the parent of node N.

We know the distance to the parent and the offset of node N with respectto the parent. We compute the coordinate (parent_x, parent_y) asfollows:parent_(—) y=y*exp(dist)parent_(—) x=x+offset*yThe point (parent_x, parent_y) is then compressed and translated toscreen coordinates.

3. Repeat step 2 until no more ancestors need to (or can) be mapped. LetM be the node farthest up the tree that is mapped.

4. Map out each child of M.

We already have the hyperbolic distance to its children and each child'soffset from the center. Let P=(x, y) be the coordinates in thehalf-plane before compression of the node M.

We compute the x coordinate for each child as follows:child_(—) y=y*exp(−dist)child_(—) x=x+offset*child_(—) yThe child coordinate (child_x, child_y) is compressed and translated tothe screen coordinate.

5. Repeat step 4 until all the visible nodes are mapped.

Unlike the original hyperbolic tree where the entire Poincaré model hasa finite size, and thus can be displayed in a finite window, thehalf-plane model has infinite size, and so is cropped for display in thewindow. The cropping for one embodiment selects a region bounded by −1and 0 in the x direction, and −1 and 1 in the y direction.

Before display, however, the half-plane model is compressed. By itself,the half-plane model has disadvantages, as illustrated in the rightvisualization of FIG. 2. It provides little contextual information aboutthe ancestors of the node in focus, and generally makes less efficientuse of screen real-estate. The invention compresses what would be on theleft in the half-plane model, both horizontally and vertically, to bringit into view. The mapping need not be conformal, or local shapepreserving. Rather, the compression should, however, preserve theverticality of siblings, or the illusion of columns.

Thus, laying out the nodes in the half-plane is not enough, as ancestorinformation is usually not visible. Thus after layout, compression isapplied to “squeeze in” the ancestors of the nodes visible. This is doneby applying a compression transformation to the node coordinates, asfollows according to a preferred embodiment.

For each point (x, y) in uncompressed half-plane, we have acorresponding point (X, Y) that is actually displayed. These are relatedby:y=Y*fx=X*fx+SLOPE*Y

-   -   where f=COMPRESS_COEFF/(COMPRESS_AXIS−Y), and    -   fx=f*f/COMPRESS_AXIS        The constants are chosen as follows:        COMPRESS_COEFF=1.0        COMPRESS_AXIS=1.075        SLOPE=0.0 or −2.7

The first number COMPRESS_COEFF controls the overall compression (highernumber means more compression). The second number COMPRESS_AXIS controlsthe rate of increase of compression as the point approaches the leftedge (the edge opposite the horizon). This number should be in the range1.01-2.0 or so (as it gets closer to 1.0, the compression increases morerapidly towards the left edge). The number 1.075 seems (afterexperimentation) to give the right amount of ancestry information. Thethird number SLOPE gives a slight slant (if non-zero) so that thechildren of a node tend to appear above or below the parent. Defaultvalue is 0.0 for no slant, or −2.7 if a slant is desired. The values canrange −10 to +10 or so for a reasonable tree.

After compression, the half-plane is clipped as described above to yieldthe rectangle that is displayed. The clipped rectangle is then scaled tofill the display window.

FIGS. 14 and 15 Illustrated the basic process for laying out a node-linkstructure in hyperbolic space, combined with mapping to a Euclideanscreen space and compression in the screen space. FIG. 14 provides abasic flow chart, and FIG. 15 provides an illustration of the parametersutilized in the layout process. Thus, the process begins with obtainingthe node-link data (block 300). For each child of a parent node, thewidth of the child is computed in hyperbolic space (block 301). Thus,with reference to FIG. 15, a particular parent node A has a set of childnodes W-Z. The node width parameter WIDTH_(H) is indicated by annotation320, and constitutes a length in a line essentially parallel with thehorizon along the width axis 310. Also, the sum of the widths WIDTH_(H)of all the children W-Z of the parent node A, plus a value SPACING_(H)indicated by annotation 321 for spacing between horocyles is computed todefine a parameter TOTAL WIDTH_(H) indicated by annotation 322 (block302). The parent-child distance parameter DIST_(H) as indicated by annotation 323 is computed based upon the TOTAL WIDTH_(H) parameter isdescribed above (block 303). The DIST_(H) parameter is a length alongthe line parallel to the depth axis 311, which is orthogonal to thehorizon. The next parameter OFFSET_(H) is computed as indicated by thean notation 324 to indicate a distance along the width axis from theposition of the parent A indicated by line 325 to the center of theparticular child node W (block 304). A data structure for a particularnode, such as node W, defines a position in the hyperbolic spacerelative to a parent node, such as node A in this example. The datastructure in this example stores the parameters DIST_(H), WIDTH_(H) andOFFSET_(H), to specify a layout in the hyperbolic space. Theseparameters can be computed and stored in advance of the display of thenode-link structure.

To display the node link structure, the nodes to be display are mappedto the screen based upon a position indicated for one node in thenode-link structure (block 305), or for a portion of the node-linkstructure to be displayed. Using the data structures that specify aposition of nodes relative to other nodes, starting with the positionindicated for the particular node, in an iterative fashion, the entireportion of the node-link structure to be displayed is mapped into aEuclidean space. Finally, a compression transformation is applied to thecoordinates of the nodes as described above to position the nodes in thedisplay area (block 306).

Since user interaction is in terms of the compressed display, userclicks must be transformed back to the uncompressed coordinates to beinterpreted. The formulas which invert the compression mapping are:

Decompression (Screen-->Half Plane Model)x′=x*f+SLOPE*yy′=y*k/(1.01−y)Under compression, the links to children get progressively steeper forsiblings further from the focus. This presents a potential problem, asthere is a tendency for links from ancestors to clutter the display. Thepreferred embodiment solves this by not drawing links to nodes that arefar above or below the clipping region, even though part of the linkswould be visible.

The sense of siblings, and of nodes of the same level that do not sharea parent, lining up in columns carries over to the design of the userinteraction. The interaction is explicitly aware of the layout ofsiblings along lines parallel to the horizon, and strengthens that senseof the significance of the layout of the siblings. In particular, userinteractions leave the relative positions of the lines of siblings fixedunless there is a strong user indication that the contrary is desired.The invention does this by adjusting its interpretation of theinteraction depending on which column the interaction deals with.Further, mouse operations toward the horizon and compressed edges areclipped toward the middle to prevent a small mouse movement from havingan excessive consequence. This is analogous to the treatment by theoriginal hyperbolic tree, translated to the present invention.

In particular, mouse clicks or drags that are within a threshold, forexample, 5% of the total depth from a border parallel to the horizon aretreated as if they were a predetermined distance, for example, 5% awayfrom the border. Mouse drags that are 90% vertical are treated as ifthey were completely vertical. Mouse clicks on a position to requestcentering of that position will affect only the vertical position, andnot the horizontal position if the position is already within the middleregion, for example the middle 50%, of the horizontal span of thedisplay.

Thus, the user interaction promotes the sense that the nodes forms“columns” when the horizon is vertical. This is done in one preferredembodiment by preserving the location of the column wheneverappropriate.

FIG. 16 shows a display area 350 which is divided into regions for thepurposes of managing user interaction according to one example of thepresent invention. The display area 350 has a screen width indicated bythe annotation 360 and a screen height indicated by the annotation 361.In this example, the horizon of the hyperbolic space corresponds withthe right-hand side 351 of the display area 350. The display area has aside 352 opposite the horizon. Also, the display area has a top side 353and the bottom side 354. The screen area 350 is divided into top andbottom halves by a center axis 355 which is orthogonal to the horizon.The screen area 350 is divided into a first region between the leftvertical line 356 and the left side 352, the second region between rightvertical line 357 and the right side 351, and a central region betweenthe first and second regions. In addition, a line 358 is parallel withand spaced away from the right side by a threshold amount, such as 5percent of the total screen width as mentioned above. Likewise, avertical line 359 is parallel with an spaced away from the left side bya threshold amount, such as 5 percent of the total screen width.

Suppose a node is clicked. Then it will be moved, in one example system,as follows:

1. If the node is in the center region(s), the node position is adjustedto (or near) the mid line 355, centering it in the same column. Hencethe movement is purely vertical.

2. If the node is in the right side region, usually corresponding to acolumn descendant from a node in the center region, the node position isadjusted just enough to display its children.

3. If the node is in the left side region, usually corresponding to anancestry column or node, the node position is adjusted to the left edgeof the center region.

These creates an illusion that the nodes are organized in columns, andenables the user to quickly riffle though the nodes in the same column.Mouse actions are clipped near both left and right edges, and optionallyon the top and bottom edges, to avoid rapid movement of the tree.

FIGS. 17 and 18 show flow charts for example algorithms for filteringinput signals which indicate positions on the display area, such asdisplay area 350 shown in FIG. 16. In FIG. 17, the process begins if theposition of the pointer, after the position has been clipped to athreshold distance from a side parallel to the horizon if necessary, ison a node (block 400). The node indicated is centered vertically in thescreen (block 401). Next, the horizontal position is determined (block402). The process determines whether the position is in the ancestorregion on the left-hand side (block 403). If the position is in theancestor region, then the node position is adjusted to the left edge ofthe center region (block 404) and the process ends (block 405). If atnode 403, it was determined that the position was not in the ancestorregion, the process determines whether there is room between theposition and horizon for painting children nodes of the node indicated(block 406). If there is room, then the position of the node relative tothe horizon is left alone (block 407), and process ends (block 405). Ifat block 406, it is determined that there is not room to paint thechildren on the display area, then the node position is adjusted awayfrom the horizon to make room for the children (block 408), and theprocess ends (block 405).

In FIG. 18, the process begins if the position of the pointer, after theposition is clipped to a threshold distance from a side parallel to thehorizon if necessary, is not on a node (block 410). In this case, aninput signal indicating a position is computed. First, the position iscentered vertically in the display area (block 411). Next, thehorizontal position within the display area is determined (block 412).The process determines whether the position is in the ancestor region onthe left side of the screen (block 413). If it is the ancestor region,then the position is moved to the left edge of the center region (block414). The process ends at block 415. If at block 413, the position wasnot found in the ancestor region, then the process determines whetherthe position is in the child region on the right side the screen area(block 416). If position is not in the child region, then the horizontalposition is not changed (block 417) and the process ends (block 415). Ifat block 416 it is determined that the position is in the child region,then the position is moved to the right edge of the center region (block418) and the process ends (block 415).

The above embodiments are not the only possible embodiments. Analternative embodiment would get much of the same appearance withoutmapping to hyperbolic geometry at all, but just by placing nodes incolumns of various widths, and redoing the placement with each change offocus. But that embodiment is not preferred, as it turns out to becomplicated to implement, and doesn't work as well with incrementalloading of the tree data.

The asymmetry between horizontal and vertical directions also enables adual-focus visualization, where the stretch factor in the verticaldimension varies, as in the table lens, to allow separated parts of thetree to be in focus.

Computer program listings expressed in the Java language with commentsfor the layout, mapping, compression/decompression, and user interactionare provided below. Persons of skill in the art will understand that thecomputer program listings are representative of one example method, andare useful in teaching an implementation an embodiment of the presentinvention. Many other techniques can be utilized.

Code for Layout of the Tree—Copyright, Inxight Software, Inc. 2001.

/** Amount of hyperbolic space to give to the root.     */ privatestatic final double ROOT_WIDTH = 1.5; /** Minimum amount of space a nodeshould get.      */ private static final double MIN_WIDTH = 0.20; /**Amount of spacing to leave between siblings,  in addition to what eachsibling needs.     */ private static final double SPACING = 0.15; /**Minimum parent-child distance allowed.      */ private static finaldouble MIN_DIST = 1.2; /** Default parent-child distance.        */private static final double DEFAULT_DIST = 1.0; /**  * Lays out theroot.  */ Object layoutRoot(int nrChildren) {  // This just gives theroot node a default width given by root_width,  // usually 1.5, but canvary (by stretch factor) from around 0.15 to  // 15.  HalfPlaneDatarootData = new HalfPlaneData(0.0, 0.0, root_width);  rootData.aboveSpace= rootData.belowSpace  = rootData.sideSpace = default_dist;  returnrootData; } /**  * Lays out the children of the given parent. The numberof children  * for each child is passed in the array nrGrandChildren. */ boolean layoutChildren(Object parentData, int [ ] nrGrandChildren,    Object [ ] childrenData) {  // NOTE: All distances used here arehyperbolic distance. boolean layoutChanged = false; int nrChildren =nrGrandChildren.length; if (nrChildren == 0)  return false; // no child,just return. // Half-widths allocated to each child. double [ ] widths =new double[nrChildren]; // Position of each child. double [ ] pos = newdouble[nrChildren]; double totalWidth; // total width requested by thechildren. double width; totalWidth = 0.0; for (int i = 0; i <nrChildren; i++) {  if (! (childrenData[i] instanceof HalfPlaneData)) childrenData[i] = new HalfPlaneData( );  // Compute the half-width forthe i-th children. Give each child  // at least some minimal distance,indicated by min_width  // (usually 0.2, but can be adjusted, say in therange 0.02–2.0).  // Using the function asinh is somewhat arbitrary, anyfunction  // with logarithmic increase would work fine.  width =Math.max(min_width,     0.5 * asinh(nrGrandChildren[i] * 0.2));  //Update the width / position arrays.  widths[i] = width;  totalWidth +=width;  pos[i] = totalWidth;  totalWidth += width; } totalWidth *= 0.5;HalfPlaneData parent = (HalfPlaneData) parentData; // Compute theparent-child distance. double dist = Math.max(min_dist,     Math.log((totalWidth + spacing) / parent.width)); // Now computethe offset for each child. Offset is the distance // of each child fromthe mid-point. Also calculate the space each // node has. doubleoldWidth; HalfPlaneData child; for (int i = 0; i < nrChildren; i++) { child = (HalfPlaneData) childrenData[i];  child.offset = pos[i] −totalWidth;  oldWidth = child.width;  width = widths[i];  child.width =width;  if (Math.abs(width − oldWidth) > 0.000001)  layoutChanged =true;  child.sideSpace = width;  child.aboveSpace = 0.5 * dist; parent.belowSpace = 0.5 * dist;  child.belowSpace = default_dist * 2.0; }  parent.dist = dist;  return layoutChanged; }Code for Mapping Procedure—Copyright, Inxight Software, Inc. 2001.

/**  * Assuming that the child is mapped, map the parent.  */ booleanmapParent(Object parentData, Object childData) {  HalfPlaneData parent =(HalfPlaneData) parentData;  HalfPlaneData child = (HalfPlaneData)childData;  Complex dst = moveVertical(moveHorizontal(child.pt,−child.offset),       −parent.dist);  parent.pt = dst;  parent.pt2 =compress(dst);  parent.winPt = compressedPlaneToWindow(parent.pt2); return isVisible(parent); } /**  * Assuming that the parent is mapped,map the child.  */ boolean mapChild(Object parentData, Object childData){  HalfPlaneData parent = (HalfPlaneData) parentData;  HalfPlaneDatachild = (HalfPlaneData) childData;  Complex dst =moveHorizontal(moveVertical(parent.pt, parent.dist),      child.offset);  child.pt = dst;  child.pt2 = compress(dst); child.winPt = compressedPlaneToWindow(child.pt2);  returnisVisible(child); } /* Move hyperbolic distance d from point pt parallelto the  real axis.        */ private Complex moveHorizontal(Complex pt,double d) {  return new Complex(pt.real + d*pt.imag, pt.imag); } /* Movehyperbolic distance d from point pt parallel to the  imaginary axis.Displacement is positive toward the horizon  (the real axis).       */private Complex moveVertical(Complex pt, double d) {  return newComplex(pt.real, pt.imag * Math.exp(−d)); }Code for Compression/Uncompression—Copyright, Inxight Software, Inc.2001.

// Constants used by the compression routines private static finaldouble COMPRESS_COEFF = 1.0; private static final double COMPRESS_AXIS =1.075; /**  * Converts a point in compressed half-plane intocorresponding  * point in the true half-plane. */ Complexuncompress(Complex z) {  // The point (x, y) in the compressedhalf-plane is converted to  // corresponding point (xx, yy) in the truehalf-plane.  double x = z.real;  double y = z.imag;  // Uncompressionfactor for the y coordinate. As y approaches  // 1.0, f becomes verylarge.  double f = COMPRESS_COEFF / (COMPRESS_AXIS − y);  //Uuncompression factor for the x coordinate (this is same as  // thederivative df/dy, in order to have same compression ratio  // locally). double fx = f * f / COMPRESS_COEFF;  // Multiply by the uncompressionfactor calculated.  double xx = x * fx;  double yy = y * f;  return newComplex(xx, yy); } /**  * Converts a point in the half-plane intocorresponding point in the  * compressed half-plane.  */ Complexcompress(Complex z) {  // The point (x, y) in the true half-plane isconverted to the  // corresponding point (xx, yy) in the compressedhalf-plane.  double x = z.real;  double y = z.imag;  // The followingformulas are just the inverse formula found in the  // uncompressformula.  yy = COMPRESS_AXIS * y / (COMPRESS_COEFF + y);  double f =COMPRESS_COEFF / (COMPRESS_AXIS − yy);  f = f * f / COMPRESS_COEFF;  xx= x/f;  return new Complex(x, y); }Code for User Interaction—Copyright, Inxight Software, Inc. 2001.

/**  * The user clicked on the given node. Determines where to put  *the node.  */ Point getOptimalPosition(Object nodeData) {  HalfPlaneDatanode = (HalfPlaneData) nodeData;  Point winPt = node.winPt;  Complex Pt= node.pt;  double dist = node.dist;  int left = width / 3;  int x, y; y = height / 2; // center the node vertically.  x = winPt.x;  double c= moveVertical(pt.imag, dist);  if

<= paintableHorizon * 1.5) {   // if the location of the children iswithin 1.5 times the   // paintable horizon, move children to at least2.0 times the paintable   // horizon. Paintable horizon is the distancefrom the right edge of the   // screen to the left of which the nodesare considered “paintable”.   // It is (rather arbitrarily) set to 24screen pixels.   c = moveVertical(paintableHorizon * 2.0, −dist);  Point p = planeToWindow(new Complex(0.0, c));   x = p.x; } else if(winPt.x < left)   // if the node is in the ancestry section, move ittowards the center.   x = left;   return new Point(x, y); } /**  * Theuser clicked on a point not in a node. Determines where to  * put thepoint.  */ Point getOptimalPosition(Point winPt) {  int left = width /3;  int right = left * 2;  int x, y;  y = height / 2; // center thepoint vertically  x = winPt.x;  // Just move toward the center(horizontally) it the point is too  // near the edge.  if (x < left)  x= left;  else if (x > right)  x = right;  return new Point(x, y); }

While the present invention is disclosed by reference to the preferredembodiments and examples detailed above, it is to be understood thatthese examples are intended in an illustrative rather than in a limitingsense. It is contemplated that modifications and combinations willreadily occur to those skilled in the art, which modifications andcombinations will be within the spirit of the invention and the scope ofthe following claims.

1. A computer implemented method for providing a displayablerepresentation of a hierarchy, comprising; laying out the hierarchy in ahyperbolic space to produce hyperbolic layout data for the hierarchy;using a half-plane model with compression to map a portion of thehyperbolic layout data for the hierarchy to display layout data, whereinusing the half-plane model includes defining a horizon and a horocycleto preserve vertical alignment of the displayable representation; andstoring or transmitting said display layout data for use in displayingsaid displayable representation.
 2. The method of claim 1, wherein thehierarchy comprises a node-link structure, and the hyperbolic layoutdata comprises a data structure associated with a node in the node-linkstructure which includes parameters specifying a position in thehyperbolic space relative to a parent node.
 3. The method of claim 1,wherein said using a half-plane model with compression includes: mappingthe portion of the hyperbolic layout data to an Euclidean spaceaccording to a half-plane model to produce Euclidean layout data; andcompressing the Euclidean layout data to yield the display layout datato provide a displayable representation of the portion of the hierarchy.4. The method of claim 3, wherein the display layout data provides adisplayable representation arranged for display in a substantiallyrectangular form factor.
 5. The method of claim 1, wherein said layingout the hierarchy in a hyperbolic space includes: for each particularnode in the hierarchy to be displayed, determining a distance along afirst axis between a parent node and the particular node, anddetermining an offset along a second axis from the parent node and theparticular node.
 6. The method of claim 1, wherein said laying out thehierarchy in a hyperbolic space, the hyperbolic space including ahorizon, includes: for each particular node in the hierarchy to bedisplayed, determining a distance along a first axis generallyperpendicular to the horizon between a parent node and the particularnode, and determining an offset along a second axis generally parallelto the horizon from the parent node and the particular node, where saiddetermining a distance includes determining a number of child nodesassociated with the parent, assigning a width along the second axis foreach of said child nodes, and computing said distance in response to thewidths of said child nodes.
 7. The method of claim 1, wherein saidlaying out the hierarchy in a hyperbolic space, the hyperbolic spaceincluding a horizon, includes: for each particular node in the hierarchyto be displayed, determining a distance along a first axis generallyperpendicular to the horizon between a parent node and the particularnode, and determining an offset along a second axis generally parallelto the horizon from the parent node and the particular node, where saiddetermining a distance includes determining a number of child nodesassociated with the parent, assigning a width along the second axis foreach of said child nodes, and computing said distance in response to thewidths of said child nodes, so that there is enough space along saidsecond axis to layout said child nodes, including said particular node,with the assigned widths.
 8. The method of claim 1, wherein thehierarchy comprises a node-link structure, and the hyperbolic layoutdata comprises a data structure associated with a node in the node-linkstructure which includes parameters specifying a position in thehyperbolic space relative to another node, and wherein said using ahalf-plane model with compression to map a portion of the hyperboliclayout data for the hierarchy to display layout data, includesdetermining a position in one of said hyperbolic space and saidEuclidean space, finding a position of a first node in said hierarchyclose to said position, and then computing the positions of other nodesin said hierarchy relative to said first node using said hyperboliclayout data.
 9. The method of claim 1, wherein the hierarchy comprises anode-link structure, and the hyperbolic layout data comprises a datastructure associated with a node in the node-link structure whichincludes parameters specifying a position in the hyperbolic spacerelative to another node, and wherein said using a half-plane model withcompression to map a portion of the hyperbolic layout data for thehierarchy to display layout data, includes determining a position of afirst node in one of said hyperbolic and said Euclidean space, and thencomputing the positions of other nodes in said hierarchy relative tosaid first node.
 10. A computer implemented method for providing adisplayable representation of a hierarchy, comprising; storinghyperbolic layout data specifying positions of nodes in the hierarchy ina hyperbolic space; accepting user input indicating a portion of saidhierarchy for display; using a half-plane model with compression to mapsaid portion of the hyperbolic layout data for the hierarchy intodisplay layout data, wherein using the half-plane model includesdefining a horizon and a horocycle to preserve vertical alignment of thedisplayable representation; and using said display layout data todisplay said displayable representation.
 11. The method of claim 10,wherein the hierarchy comprises a node-link structure, and thehyperbolic layout data comprises a data structure associated with a nodein the node-link structure which includes parameters specifying aposition in the hyperbolic space relative to a parent node.
 12. Themethod of claim 10, wherein said using a half-plane model withcompression includes: mapping the portion of the hyperbolic layout datato an Euclidean space according to a half-plane model to produceEuclidean layout data; and compressing the Euclidean layout data toyield the display layout data.
 13. The method of claim 12, wherein thedisplay layout data provides a displayable representation arranged fordisplay in a substantially rectangular form factor.
 14. The method ofclaim 10, wherein said laying out the hierarchy in a hyperbolic space,the hyperbolic space including a horizon, includes: for each particularnode in the hierarchy to be displayed, determining a distance along afirst axis generally perpendicular to the horizon between a parent nodeand the particular node, and determining an offset along a second axisgenerally parallel to the horizon from the parent node and theparticular node.
 15. The method of claim 10, wherein said laying out thehierarchy in a hyperbolic space, the hyperbolic space including ahorizon, includes: for each particular node in the hierarchy to bedisplayed, determining a distance along a first axis generallyperpendicular to the horizon between a parent node and the particularnode, and determining an offset along a second axis generally parallelto the horizon from the parent node and the particular node, where saiddetermining a distance includes determining a number of child nodes,including the particular node, associated with the parent, assigning awidth along the second axis for each of said child nodes, and computingsaid distance in response to the widths of said child nodes.
 16. Themethod of claim 10, wherein said laying out the hierarchy in ahyperbolic space, the hyperbolic space including a horizon, includes:for each particular node in the hierarchy to be displayed, determining adistance along a first axis generally perpendicular to the horizonbetween a parent node and the particular node, and determining an offsetalong a second axis generally parallel to the horizon from the parentnode and the particular node, where said determining a distance includesdetermining a number of child nodes, including said particular node,associated with the parent, assigning a width along the second axis foreach of said child nodes, and computing said distance in response to thewidths of said child nodes, so that there is enough space along saidsecond axis to layout said child nodes, including said particular node,with the assigned widths.
 17. The method of claim 10, wherein thehierarchy comprises a node-link structure, and the hyperbolic layoutdata comprises a data structure associated with a node in the node-linkstructure which includes parameters specifying a position in thehyperbolic space relative to another node, and wherein said acceptinguser input includes receiving an indication of a position in one of saidhyperbolic space and said Euclidean space, finding a position of a firstnode in said hierarchy close to said indicated position, and thencomputing the positions of other nodes in said hierarchy relative tosaid first node, and displaying a changed representation based upon theposition of said first node and of said other nodes.
 18. The method ofclaim 10, wherein the hierarchy comprises a node-link structure, and thehyperbolic layout data comprises a data structure associated with a nodein the node-link structure which includes parameters specifying aposition in the hyperbolic space relative to another node, and whereinsaid accepting user input includes receiving an indication of a positionof a first node in one of said hyperbolic and said Euclidean space, andthen computing the positions of other nodes in said hierarchy relativeto said first node and displaying a changed representation based uponthe position of said first node and of said other nodes.
 19. The methodof claim 10, including displaying said displayable representation in adisplay area, wherein said accepting user input includes: acceptingsignals pointing to a location in said display area; and filtering saiduser input in response to said location in said display area to indicatea position in said hyperbolic space.
 20. The method of claim 10,including displaying said displayable representation in a display areahaving side corresponding to a horizon in the hyperbolic space, whereinsaid accepting user input includes: accepting signals pointing to alocation in said display area; and filtering said user input in responseto said location in said display area to indicate a position in saidhyperbolic space, including if said location is within a thresholddistance in Euclidean space from the horizon, then signaling a positionat a location spaced away from said side corresponding to the horizon.21. The method of claim 10, including displaying said displayablerepresentation in a display area having a first side corresponding to ahorizon in the hyperbolic space, a second side opposite the horizon, afirst region adjacent said first side, a second region adjacent saidsecond side, and a third region between “the first and second regions,wherein said accepting user input includes: accepting signals pointingto a location for a node in said display area; and filtering said userinput in response to said location in said display area to indicate aposition in said hyperbolic space, including if said location is withinsaid first region, then signaling a position at a location sufficientlyspaced away from said first side and to allow for display of a child ofsaid node within said display area.
 22. The method of claim 10,including displaying said displayable representation in a display areahaving a first side corresponding to a horizon in the hyperbolic space,and a second side opposite the horizon, wherein said accepting userinput includes: accepting signals pointing to a location for a node insaid display area; and filtering said user input in response to saidlocation in said display area to indicate a position in said hyperbolicspace, including if said location is within a threshold distance of thefirst side, then signaling a position at a location spaced away fromsaid first side by a predetermined distance.
 23. The method of claim 10,including displaying said displayable representation in a display areahaving a first side corresponding to a horizon in the hyperbolic space,and a second side opposite the horizon, wherein said accepting userinput includes: accepting signals pointing to a location for a node insaid display area; and filtering said user input in response to saidlocation in said display area to indicate a position in said hyperbolicspace, including if said location is within a threshold distance of thesecond side, then signaling a position at a location spaced away fromsaid second side by a predetermined distance.
 24. The method of claim10, including displaying said displayable representation in a displayarea having a first side corresponding to a horizon in the hyperbolicspace, a second side opposite the horizon, a first region adjacent saidfirst side, a second region adjacent said second side, and a thirdregion between the first and second regions, wherein said accepting userinput includes: accepting signals pointing to a location for a nodehaving a first representation located in said third region in saiddisplay area; and filtering said user input in response to said locationin said display area to indicate a position in said hyperbolic space,including if said location for said node is within said third region,then signaling a position which results in display of a secondrepresentation of said node at a location which is shifted substantiallyvertically within said display area from said first representation. 25.A method comprising: obtaining node-link data defining a node-linkstructure; using the node-link data to obtain layout data in a layoutspace having a negative curvature according to a half-plane model ofhyperbolic space, wherein using the half-plane model includes defining ahorizon and a horocycle; using the layout data to create arepresentation of said node-link structure by mapping said layout dataonto a display region while preserving vertical alignment of therepresentation, wherein said mapping includes compressing said layoutdata; and displaying said representation of said node-link structure.26. The method of claim 25, wherein said node-link structure includes aplurality of levels, and said mapping includes arranging nodes in thenode-like structure so that nodes in a particular level in saidplurality of levels in columns in the display region.